In order to exchange messages with each other, applications running on different computing devices in a communication network may make use of application-layer connectivity provided by a connectivity fabric of that communication network. At the transport layer, a message being sent from an initiator device to a target device may be segmented at the initiator, and the segments may be encapsulated in packets for transmission to the target during a packet transfer process. If multiple devices send messages to a target device, multiple packet transfer processes may concurrently pend at the target device.